12 research outputs found
Spectral expansion for finite temperature two-point functions and clustering
Recently, the spectral expansion of finite temperature two-point functions in
integrable quantum field theories was constructed using a finite volume
regularization technique and the application of multidimensional residues. In
the present work, the original calculation is revisited. By clarifying some
details in the residue evaluations, we find and correct some inaccuracies of
the previous result. The final result for contributions involving no more than
two particles in the intermediate states is presented. The result is verified
by proving a symmetry property which follows from the general structure of the
spectral expansion, and also by numerical comparison to the discrete finite
volume spectral sum. A further consistency check is performed by showing that
the expansion satisfies the cluster property up to the order of the evaluation.Comment: 38 pages, 1 eps figure
Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin
In this note we construct Q-operators for the spin s open Heisenberg XXX
chain with diagonal boundaries in the framework of the quantum inverse
scattering method. Following the algebraic Bethe ansatz we diagonalise the
introduced Q-operators using the fundamental commutation relations. By acting
on Bethe off-shell states and explicitly evaluating the trace in the auxiliary
space we compute the eigenvalues of the Q-operators in terms of Bethe roots and
show that the unwanted terms vanish if the Bethe equations are satisfied.Comment: 17 page
Regge spectroscopy of higher twist states in supersymmetric Yang-Mills theory
We study a family of higher-twist Regge trajectories in
supersymmetric Yang-Mills theory using the Quantum Spectral Curve. We explore
the many-sheeted Riemann surface connecting the different trajectories and show
the interplay between the degenerate non-local operators known as horizontal
trajectories. We resolve their degeneracy analytically by computing the first
non-trivial order of the Regge intercept at weak coupling, which exhibits new
behaviour: it depends linearly on the coupling. This is consistent with our
numerics, which interpolate all the way to strong coupling.Comment: main text: 6 pages, 5 figures; supplemental material: 17 pages, 3
figures, 3 table
Finite volume form factors in integrable theories
We develop a new method to calculate finite size corrections for form factors
in two-dimensional integrable quantum field theories. We extract these
corrections from the excited state expectation value of bilocal operators in
the limit when the operators are far apart. We elaborate the finite size
effects explicitly up to the 3rd L\"uscher order and conjecture the structure
of the general form. We also fully recover the explicitly known massive fermion
finite volume form factors.Comment: 37 pages, 9 figure
Entanglement Content of Quantum Particle Excitations III. Graph Partition Functions
We consider two measures of entanglement, the logarithmic negativity and the entanglement entropy, between regions of space in excited states of many-body systems formed by a finite number of particle excitations. In parts I and II of the current series of papers, it has been shown in one-dimensional free-particle models that, in the limit of large system's and regions' sizes, the contribution from the particles is given by the entanglement of natural qubit states, representing the uniform distribution of particles in space. We show that the replica logarithmic negativity and R\'enyi entanglement entropy of such qubit states are equal to the partition functions of certain graphs, that encode the connectivity of the manifold induced by permutation twist fields. Using this new connection to graph theory, we provide a general proof, in the massive free boson model, that the qubit result holds in any dimensionality, and for any regions' shapes and connectivity. The proof is based on clustering and the permutation-twist exchange relations, and is potentially generalisable to other situations, such as lattice models, particle and hole excitations above generalised Gibbs ensembles, and interacting integrable models
Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach
We extend the branch point twist field approach for the calculation of entanglement entropies to time-dependent problems in 1+1-dimensional massive quantum field theories. We focus on the simplest example: a mass quench in the Ising field theory from initial mass m0 to final mass m. The main analytical results are obtained from a perturbative expansion of the twist field one-point function in the post-quench quasi-particle basis. The expected linear growth of the RĂ©nyi entropies at large times mt â« 1 emerges from a perturbative calculation at second order. We also show that the RĂ©nyi and von Neumann entropies, in infinite volume, contain subleading oscillatory contributions of frequency 2m and amplitude proportional to (mt)â3/2. The oscillatory terms are correctly predicted by an alternative perturbation series, in the pre-quench quasi-particle basis, which we also discuss. A comparison to lattice numerical calculations carried out on an Ising chain in the scaling limit shows very good agreement with the quantum field theory predictions. We also find evidence of clustering of twist field correlators which implies that the entanglement entropies are proportional to the number of subsystem boundary points
Q-operators for the open Heisenberg spin chain
We construct Q-operators for the open spin-View the MathML source XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary YangâBaxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots
TT-deformed 2D quantum field theories
It was noticed many years ago, in the framework of massless RG ïŹows, that the irrelevant composite operator TÂŻT, built with the components of the energy-momentum tensor, enjoys very special properties in 2D quantum ïŹeld theories, and can be regarded as a peculiar kind of integrable perturbation. Novel interesting features of this operator have recently emerged from the study of eïŹective string theory models. In this paper we study further properties of this distinguished perturbation. We discuss how it aïŹects the energy levels and one-point functions of a general 2D QFT in ïŹnite volume through a surprising relation with a simple hydrodynamic equation. In the case of the perturbation of CFTs, adapting a result by Lušscher and Weisz we give a compact expression for the partition function on a ïŹnite-length cylinder and make a connection with the exact g-function method. We argue that, at the classical level, the deformation naturally maps the action of N massless free bosons into the Nambu-Goto action in static gauge, in N + 2 target space dimensions, and we brieïŹy discuss a possible interpretation of this result in the context of eïŹective string models